Statistical mechanics of disordered systems : a mathematical perspective /
Anton Bovier.
- Cambridge : Cambridge University Press, 2006.
- 1 online resource (xiv, 312 pages) : digital, PDF file(s).
- Cambridge series on statistical and probabilistic mathematics ; 18 .
- Cambridge series on statistical and probabilistic mathematics ; 18. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Principles of statistical mechanics -- Lattice gases and spin systems -- Gibbsian formalism for lattice spin systems -- Cluster expansions -- Gibbsian formalism and metastates -- The random-field Ising model -- Disordered mean-field models -- The random energy model -- Derrida's generalized random energy models -- The SK models and the Parisi solution -- Hopfield models -- The number partitioning problem.
This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail.
9780511616808 (ebook)
Statistical mechanics. Mathematical statistics. Probabilities. System theory.